The nominally retired double agent Sergei Skripal spent several weeks in a coma after being discovered on a bench in Salisbury in March; he eventually recovered enough to be released from the hospital.
He said the "main line of inquiry" was a connection between the Skripal poisoning and the case of Rowley and Sturgess but said scientists had not been able to determine whether the nerve agent came from the same batch.
"We hope that the circumstances of her poisoning will be investigated in good faith and in accordance with high global standards, and the perpetrators will be brought to justice", the embassy said in a statement on Monday. Moscow rejects the claim.
The Minister of Interior, Sajid Javid, asked on Thursday explanations to Russian Federation by poisoning of Rowley and Sturgess, four months after government blamed Moscow for attack on Skripal. The White House later said it was expelling 60 Russian diplomats as retaliation for Moscow's alleged actions. "We consider that it is a danger not only for the British, but for other Europeans".
Peskov went on to comment on a separate statement by Russia's representative at the Organization for the Prohibition of Chemical Weapons (OPCW), Alexander Vasilievich Shulgin.More news: Top U.S. Senate Democrat vows to fight Trump's Supreme Court pick
The Russian Embassy hit back, accusing the government of trying to "muddy the waters" and "frighten its own citizens". "A proper and careful investigation for instance?" the country's official Ministry of Foreign Affairs account tweeted.
The 67-year-old ex-agent was living in Salisbury, a cathedral city 90 miles (145 kilometers) southwest of London, when he was struck down along with his daughter, Yulia, who was visiting him.
Putin has said that if a military-grade nerve agent had been used against them, the victims would have died. Authorities are still investigating the incident, which has been widely speculated to be a revenge hit by Russian intelligence services or organised crime - part of a pattern of allegedly suspicious deaths of supposed traitors to the Russian state living overseas in the UK.
On Apr 17, an operation begins to clean up affected areas of Salisbury. Rowley remains critically ill.
Counter Terror Police are keen to hear from anyone who may have information that could assist with this investigation and would urge anyone who can help to contact them by calling 0800 789 321.
Head of UK Counter Terrorism policing Neil Basu said: 'This is shocking and tragic news.More news: Thai cave rescue: Four more boys extracted in second operation
"It's Britain's problem and the problem of how interested Britain is in a real investigation", he said.
Russian Federation hit back, denouncing Britain for playing "dirty political games".
She has been formally identified as 44-year-old Dawn Sturgess, from Durrington.
They had visited Salisbury the day before they fell ill.
"Gavin Williamson's claim that Russian Federation has something to do with death of Dawn Sturgess is just the same old mantra #russiansdidit".
"Police and security officials are working urgently to establish the facts of this incident, which is now being treated as murder", May said.More news: Trump arrives in Brussels ahead of potentially contentious North Atlantic Treaty Organisation summit